library(Rssa)
Предупреждение: пакет ‘Rssa’ был собран под R версии 4.2.3
Загрузка требуемого пакета: svd
Предупреждение: пакет ‘svd’ был собран под R версии 4.2.3
Загрузка требуемого пакета: forecast
Предупреждение: пакет ‘forecast’ был собран под R версии 4.2.3
Присоединяю пакет: ‘Rssa’
Следующий объект скрыт от ‘package:stats’:
decompose
library(signal)
Предупреждение: пакет ‘signal’ был собран под R версии 4.2.3
Присоединяю пакет: ‘signal’
Следующий объект скрыт от ‘package:Rssa’:
roots
Следующие объекты скрыты от ‘package:stats’:
filter, poly
library(gsignal)
Предупреждение: пакет ‘gsignal’ был собран под R версии 4.2.3
Registered S3 methods overwritten by 'gsignal':
method from
plot.grpdelay signal
plot.specgram signal
print.freqz signal
print.grpdelay signal
print.impz signal
print.specgram signal
Присоединяю пакет: ‘gsignal’
Следующий объект скрыт ‘.GlobalEnv’:
dftmtx
Следующий объект скрыт от ‘package:signal’:
Arma, as.Arma, as.Zpg, bartlett, bilinear, blackman, boxcar, butter, buttord, cheb1ord, chebwin, cheby1, cheby2,
chirp, conv, decimate, ellip, ellipord, fftfilt, filter, filtfilt, fir1, fir2, flattopwin, freqs, freqs_plot,
freqz, freqz_plot, gausswin, grpdelay, hamming, hanning, ifft, impz, interp, kaiser, kaiserord, levinson, Ma,
medfilt1, poly, remez, resample, sftrans, sgolay, sgolayfilt, specgram, triang, unwrap, Zpg, zplane
Следующие объекты скрыты от ‘package:stats’:
filter, gaussian, poly
source("eossa_new.R")
dftmtx <- function(n) {
y <- stats::mvfft(diag(1, n))
y
}
diag_averaging <- function(A){
B <- A[nrow(A):1, ] |> Re()
lapply(split(B, -(row(B) - col(B)) ), mean) |> as.numeric()
}
shift_vector <- function(vec) {
last_element <- tail(vec, 1)
vec <- vec[-length(vec)]
shifted_vec <- c(last_element, vec)
return(shifted_vec)
}
extend <- function(x, H){
# Вычисление коэффициентов AR модели для дифференцированного ряда
N <- length(x)
p <- floor(N / 3)
dx <- diff(x)
# A <- ar(dx, order.max = p, method = "yule-walker")$ar
A <- aryule(dx, p)$a
# Правое расширение
y <- x
dy <- diff(y)
er <- signal::filter(A, 1, dy)
dy <- signal::filter(1, A, c(er, rep(0, H)))
y <- y[1] + c(0, cumsum(dy))
# Левое расширение
y <- rev(y)
dy <- diff(y)
er <- signal::filter(A,1,dy)
dy <- signal::filter(1,A,c(er, rep(0, H)))
y <- y[1] + c(0, cumsum(dy))
# Расширенный ряд
xe <- rev(y)
# Вывод результатов
xe
}
Подаётся на вход временной ряд, длина окна (если её нет, то она равна длине ряда + 1 пополам) и информация о том, нужно ли расширить ряд. Расширять ряд стоит при стохастическом тренде (Autoregressive extension (default). It is indicated for stationary and stochastic trend time series as well). Реализовано только Autoregressive extension.
На выходе список выдаётся список list(t_series, importance).
t_series — матрица, по столбцам которой располагаются временные ряды,
отвечающие за частоты (i-1)/L, где i — номер столбца, L — длина
окна.
importance — вектор, отвечающий за значимость i-ого временного ряда в
разлолжении. Чем больше значение, тем больший вклад внёс i-тый временной
ряд.
circulant_SSA <- function(ts, L = NULL, extend_flag = FALSE){
time_series <- ts
# Construct trajectory matrix
N <- length(time_series)
if (is.null(L)){
L <- (N + 1)%/%2
}
# Проверка на расширения ряда
if (extend_flag == FALSE){
H <- 0
time_series <- ts
}
else{
H <- L
time_series <- extend(ts, H)
}
X <- hankel(time_series, L)
# Number of symmetric frequency pairs around 1/2
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
# Number of frequencies <= 1/2
nft <- nf2 + abs((L %% 2) - 2)
# Decomposition
# Estimate autocovariance OK
autocov <- numeric(L)
for (m in 0:(L-1)){
autocov[[m+1]] <- sum(time_series[1:(N-m)] * time_series[(1+m):N]) / (N-m)
}
# First row of circulant matrix
circ_first_row <- numeric(L)
for (m in 0:(L-1)){
circ_first_row[[m+1]] <- (L-m)/L * autocov[[m+1]] + (m)/L * autocov[[L-m]]
}
# Build circulant matrix
S_C <- matrix(circ_first_row, nrow = 1)
shifted_vector <- circ_first_row
for (i in 2:(L)) {
shifted_vector <- shift_vector(shifted_vector)
# S_C <- rbind(S_C, as.vector(shifted_vector))
S_C <- rbind(as.vector(shifted_vector), S_C)
}
# Eigenvectors of circulant matrix (unitary base)
U <- dftmtx(L)/sqrt(L)
# Real eigenvectors (orthonormal base)
U[, 1] <- Re(U[, 1])
for (k in 1:nf2) {
u_k <- U[, k + 1]
U[, k + 1] <- sqrt(2) * Re(u_k)
U[, L + 2 - (k + 1)] <- sqrt(2) * Im(u_k)
}
if (L %% 2 != 0) {
U[, nft] <- Re(U[, nft])
}
# Eigenvalues of circulant matrix: estimated power spectral density
psd <- abs(diag(t(U) %*% S_C %*% U))
# Principal components
W <- t(U) %*% X
# Reconstruction
# Elementary reconstructed series
R <- matrix(0, nrow = N+2*H, ncol = L)
for (k in 1:L) {
R[, k] <- U[ ,k] %*% t(W[k, ]) |> diag_averaging()
}
# Grouping by frequency
# Elementary reconstructed series by frequency
Z <- matrix(0, nrow = N+2*H, ncol = nft)
Z[, 1] <- R[, 1]
# Importance of component
imp <- numeric(nft)
lambda_sm <- sum(psd)
imp[1] <- psd[1]/lambda_sm
for (k in 1:nf2) {
Z[, k + 1] <- R[, k + 1] + R[, L + 2 - (k + 1)]
imp[k+1] <- (psd[k+1] + psd[ L + 2 - (k + 1)])/lambda_sm
}
if (L %% 2 != 0) {
Z[, nft] <- R[, nft]
imp[nft] <- psd[nft] / lambda_sm
}
list(t_series = Z[(H+1):(N+H),],
importance = imp,
freq = (0:(length(imp) -1))/L
)
}
# groups - list of frequencies
grouping_cissa <- function(cissa_res, groups){
freq <- cissa_res$freq
t_series <- cissa_res$t_series
residuals <- 0
result <- setNames(as.list(rep(0, length(groups))), names(groups))
for (i in 1:length(cissa_res$freq)){
flag <- FALSE
for (name in names(groups)){
if (groups[[name]][1] <= freq[i] & freq[i] <= groups[[name]][2]){
flag <- TRUE
result[[name]] <- result[[name]] + t_series[, i]
}
}
if (flag == FALSE){
residuals <- residuals + t_series[, i]
}
}
result[["residuals"]] <- residuals
result
}
generate_ts <- function(func, n=1e3, ...){
1:n |> func(...) |> ts()
}
f_cos <- function(x, A = 1, omega = 1/4, phi = 0){
f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}
f_sin <- function(x, A = 1, omega = 1/4, phi = 3*pi/2){
f_exp_mod_harm_series(x, A, alpha = 0, omega = omega, phi = phi)
}
f_exp <- function(x, A = 1, alpha = 1){
A * exp(alpha * x)
}
f_exp_cos <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
f_exp_mod_harm_series(x, A, alpha, omega, phi)
}
f_const <- function(x, C = 0){
rep(C, length(x))
}
f_exp_mod_harm_series <- function(x, A = 1, alpha = 1, omega = 1/4, phi = 0){
A*exp(alpha*x)*cos(2*pi*omega*x + phi)
}
f_linear <- function(x, a = 1, b = 0){
a*x + b
}
mse <- function(f_true, f_reconstructed){
mean((f_true - f_reconstructed)^2)
}
n <- 96*2+5
L <- 96
f_sum <- function(x){
f_const(x, C = 1) + f_cos(x, omega = 1/12)
}
f_const |> generate_ts(n, C = 1) |>
plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
generate_ts(n, omega = 1/12) |>
lines(col="green")
f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)
c <- circulant_SSA(f_n, L = 96, extend_flag = FALSE)
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/100),
sesonal = c(1/99, 1/10)
)
)
f_C <- f_const |> generate_ts(n, C = 1)
f_c <- f_cos |> generate_ts(n, omega = 1/12)
print("Ошибки при CiSSA")
[1] "Ошибки при CiSSA"
print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2) ))
[1] "Ошибка при вычислении C = 1: 3.2e-31"
print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2) ))
[1] "Ошибка при вычислении cos(pi/12): 3.6e-30"
lines(1:n, r$trend, col="blue")
lines(1:n, r$sesonal, col="blue")
f_const |> generate_ts(n, C = 1) |>
plot(col = "green", ylim = c(-1, 2), ylab = "f_n")
f_cos |>
generate_ts(n, omega = 1/12) |>
lines(col="green")
f_sum |> generate_ts(n) |> lines(lwd = 3, col='red')
f_n <- f_sum(1:n)
s <- ssa(f_n, L = 96)
r <- reconstruct(s, groups=list(
trend = 1,
sesonal = 2:3
))
print("Ошибки при SSA")
[1] "Ошибки при SSA"
print(paste("Ошибка при вычислении C = 1: ", mse(f_C, r$trend) |> format(scientific = TRUE, digits = 2) ))
[1] "Ошибка при вычислении C = 1: 9.6e-05"
print(paste("Ошибка при вычислении cos(pi/12): ", mse(f_c, r$sesonal) |> format(scientific = TRUE, digits = 2)))
[1] "Ошибка при вычислении cos(pi/12): 9.6e-05"
lines(1:n, r$trend)
lines(1:n, r$sesonal)
n <- 96*2-1
L <- 96
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
f_sum <- function(x){
f_const(x, C = C) +
f_cos(x, omega = omega_cs) +
f_exp(x, a = a) +
f_sin(x, omega = omega_sn)
}
f_C <- f_const |> generate_ts(n, C = C)
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp |> generate_ts(n, a = a)
f_n <- f_sum(1:n)
library(xtable)
Предупреждение: пакет ‘xtable’ был собран под R версии 4.2.3
# Шаг 2: Создание примера данных
data <- data.frame(
Метод = c("SSA", "CiSSA"),
e_err = c(20, 20),
c_err = c(23, 35),
ec_err = c(20, 20),
sin_err = c (20, 20),
cos_err = c(1, 1)
)
# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-2, 10),
xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")
# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_C, col = "blue") # Компонент f_C
lines(f_c, col = "blue") # Компонент f_c
lines(f_e, col = "blue") # Компонент f_e
lines(f_s, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
groups = list(
# trend = c(0, 1/100),
trend = c(0, 1/1000),
sesonal_cos = c(1/14, 1/10),
sesonal_sin = c(1/26, 1/23)
))
data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$ec_err[2] <- mse(f_C+f_e, r$trend) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")
lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# dev.off() # завершение сохранения
s <- ssa(f_n, L)
e <- eossa(s, 1:10, k = 7)
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = c(0.001),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/11)
),
threshold = 0.1)
r <- Rssa::reconstruct(e, groups=c(list(exp = 1,
C = 2
),
g_sesonal)
)
plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))
Предупреждение в wcor.ossa(e, groups = 1:24) :
Component matrices are not F-orthogonal (max F-cor is 0.93). W-cor matrix can be irrelevant
data$c_err[1] <- mse(f_C, r$C) |> formatC(format = "e", digits = 1)
data$e_err[1] <- mse(f_e, r$exp) |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)
data$ec_err[1] <- mse(f_C+f_e, r$C+r$exp) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-2, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")
lines(1:n, r$trend, type = "l", col="green")
lines(1:n, r$exp, type = "l", ylim= c(-2, 10), col="blue")
lines(1:n, r$C, col = "blue")
lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")
# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)
% latex table generated in R 4.2.2 by xtable 1.8-4 package
% Mon Nov 4 13:25:09 2024
\begin{table}[ht]
\centering
\begin{tabular}{llllll}
\hline
Метод & e\_err & c\_err & ec\_err & sin\_err & cos\_err \\
\hline
SSA & 2.2e-25 & 2.2e-25 & 4.2e-28 & 3.8e-29 & 1.6e-29 \\
CiSSA & 20 & 35 & 3.5e-02 & 1.4e-04 & 1.9e-03 \\
\hline
\end{tabular}
\caption{Example Table}
\end{table}
n <- 96*2-1
L <- 96
eps <- 1/(L+1)
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
omega_exp <- 1/48
f_sum <- function(x){
f_cos(x, omega = omega_cs) +
f_exp_mod_harm_series(x, a = a, omega = omega_exp) +
f_sin(x, omega = omega_sn)
}
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp_mod_harm_series |> generate_ts(n, a = a, omega = omega_exp)
f_n <- f_sum(1:n)
library(xtable)
# Шаг 2: Создание примера данных
data <- data.frame(
Метод = c("SSA", "CiSSA"),
exp_err = c(20, 20),
sin_err = c (20, 20),
cos_err = c(1, 1)
)
# Отрисовка ряда f_n
plot(f_n, type = "l", lwd = 3, col = 'red', ylim = c(-10, 10),
xlab = "Время", ylab = "Значения ряда", main = "Разложение временного ряда")
# Добавление отдельных компонентов (f_C, f_c, f_e)
lines(f_c, col = "blue") # Компонент f_c
lines(f_e, col = "blue") # Компонент f_e
lines(f_s, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/26-eps),
sesonal_cos = c(1/14, 1/10),
sesonal_sin = c(1/26, 1/23)
))
data$cos_err[2] <- mse(f_s, r$sesonal_sin) |> formatC(format = "e", digits = 1)
data$sin_err[2] <- mse(f_c, r$sesonal_cos) |> formatC(format = "e", digits = 1)
data$exp_err[2] <- mse(f_e, r$trend) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/CiSSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "CiSSA разложение временного ряда")
lines(1:n, r$trend, col = "blue")
lines(1:n, r$sesonal_sin, col = "blue")
lines(1:n, r$sesonal_cos, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# dev.off() # завершение сохранения
s <- ssa(f_n, L)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = c(1/25-eps),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/11)
),
threshold = 0.1)
r <- reconstruct(e, groups= g_sesonal)
plot(wcor(e, groups = 1:24), scales = list(at = c(10, 20, 30)))
Предупреждение в wcor.ossa(e, groups = 1:24) :
Component matrices are not F-orthogonal (max F-cor is -0.529). W-cor matrix can be irrelevant
data$exp_err[1] <- mse(f_e, r$trend) |> formatC(format = "e", digits = 1)
data$cos_err[1] <- mse(f_c, r$sesonal1) |> formatC(format = "e", digits = 1)
data$sin_err[1] <- mse(f_s, r$sesonal2) |> formatC(format = "e", digits = 1)
# png("C:/Users/nik1m/Desktop/уник/6 сем/курсач/Текст работы/img/trend inseparability/SSA.png") # сохранение в формате PNG
plot(1:n, f_n, type = "l", lwd=3, ylim= c(-10, 10), col="red",
xlab = "Время", ylab = "Значения ряда", main = "SSA разложение временного ряда")
lines(1:n, r$trend, type = "l", col="blue")
lines(1:n, r$sesonal1, col = "blue")
lines(1:n, r$sesonal2, col = "blue")
# Легенда
legend("topleft", legend = c("Весь ряд", "Компоненты"),
col = c("red", "blue"), lty = 1, lwd = 3)
# Шаг 3: Преобразование данных в формат LaTeX
table_latex <- xtable(data, caption = "Example Table")
# Шаг 4: Вывод таблицы в LaTeX файл
print(table_latex, include.rownames = FALSE)
% latex table generated in R 4.2.2 by xtable 1.8-4 package
% Mon Nov 4 13:25:10 2024
\begin{table}[ht]
\centering
\begin{tabular}{llll}
\hline
Метод & exp\_err & sin\_err & cos\_err \\
\hline
SSA & 4.7e-29 & 1.1e-29 & 8.4e-30 \\
CiSSA & 3.2e-02 & 2.6e-04 & 5.8e-03 \\
\hline
\end{tabular}
\caption{Example Table}
\end{table}
library(readxl)
Предупреждение: пакет ‘readxl’ был собран под R версии 4.2.3
data <- read_excel("Data/International_Financial_Statistics_.xlsx")
New names:
• `` -> `...2`
• `` -> `...3`
• `` -> `...4`
• `` -> `...5`
• `` -> `...6`
• `` -> `...7`
• `` -> `...8`
• `` -> `...9`
• `` -> `...10`
• `` -> `...11`
• `` -> `...12`
• `` -> `...13`
• `` -> `...14`
• `` -> `...15`
• `` -> `...16`
• `` -> `...17`
• `` -> `...18`
• `` -> `...19`
• `` -> `...20`
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data |> head()
Отрисовка данных IP
dates <- seq(as.Date("1970-01-01"), as.Date("2018-1-30"), by = "month")
IP_values <- data[2, -c(1, 2)] |> as.double()
plot(dates, IP_values, type="l")
Отрисовка трендовой составляющей чёрным цветом, основной временной ряд — красным
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = TRUE)
r <- c$t_series
r <- grouping_cissa(c,
groups = list(
trend = c(0, 1/192),
cycle = c(1/97, 5/95),
sesonal = c(1/13, 1/2+0.0001)
)
)
r_sesonal <- grouping_cissa(c,
groups = list(
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
)
)
# cissa_trend <- r[,1] + r[,2]
# cissa_cycle <- r[, 3:11] |> rowSums()
# cissa_sesonal <- r[, c(17, 33, 49, 65, 81, 97)] |> rowSums()
# cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)
cissa_trend <- r$trend
cissa_cycle <- r$cycle
cissa_sesonal <- Reduce("+", r_sesonal |> within(rm(residuals)))
cissa_residuals <- IP_values_slice - (cissa_trend + cissa_cycle + cissa_sesonal)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, cissa_trend,
type="l", col = "red")
plot(dates_slice, cissa_cycle,
type="l", col = "red")
plot(dates_slice, cissa_sesonal,
type="l", col = "red")
plot(dates_slice, cissa_residuals,
type="l", col = "red")
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, cissa_trend+cissa_cycle+cissa_sesonal,
type="l", col = "red")
s <- ssa(IP_values_slice, L = 192)
e <- fossa(s)
# e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
eps <- 1/193
groups <- grouping.auto(e,
freq.bins = list(trend = c(1/192),
cycle = c(1/97, 5/95),
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
),
threshold = 0)
plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
main = "W-correlation matrix SSA (fossa)")
r <- reconstruct(e, groups=groups)
ssa_trend_f <- r$trend
ssa_cycle_f <- r$cycle
ssa_sesonal_f <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals_f <- IP_values_slice - (ssa_trend_f + ssa_cycle_f + ssa_sesonal_f)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, ssa_trend_f,
type="l", col = "magenta")
plot(dates_slice, ssa_cycle_f,
type="l", col = "magenta")
plot(dates_slice, ssa_sesonal_f,
type="l", col = "magenta")
plot(dates_slice, ssa_residuals_f,
type="l", col = "magenta")
library(Rssa)
source("eossa_new.r")
s <- ssa(IP_values_slice, L = 192)
e <- eossa_new(s, nested.groups = list(1:30), clust_type = "distance")
groups <- grouping.auto(e,
freq.bins = list(trend = c(1/192),
cycle = c(1/97, 5/95),
s1 = c(16/192 - eps, 16/192 + eps),
s2 = c(32/192 - eps, 32/192 + eps),
s3 = c(48/192 - eps, 48/192 + eps),
s4 = c(64/192 - eps, 64/192 + eps),
s5 = c(80/192 - eps, 80/192 + eps),
s6 = c(96/192 - eps, 96/192 + eps)
),
threshold = 0)
plot(wcor(e, groups = 1:30), scales = list(at = c(10, 20, 30)),
main = "W-correlation matrix SSA (eossa)")
Предупреждение в wcor.ossa(e, groups = 1:30) :
Component matrices are not F-orthogonal (max F-cor is -0.0621). W-cor matrix can be irrelevant
r <- reconstruct(e, groups=groups)
ssa_trend <- r$trend
ssa_cycle <- r$cycle
ssa_sesonal <- r$s1 + r$s2 + r$s3 + r$s4 + r$s5 + r$s6
ssa_residuals <- IP_values_slice - (ssa_trend + ssa_cycle + ssa_sesonal)
plot(dates_slice, IP_values_slice,
type="l", col = "black")
lines(dates_slice, ssa_trend,
type="l", col = "blue")
plot(dates_slice, ssa_cycle,
type="l", col = "blue")
plot(dates_slice, ssa_sesonal,
type="l", col = "blue")
plot(dates_slice, ssa_residuals,
type="l", col = "blue")
plot(dates_slice, IP_values_slice,
main = "IP USA тренд",xlab = "Время", ylab = "Значение",
type="l", col = "black")
lines(dates_slice, ssa_trend,
type="l", col = "blue", lwd=2)
lines(dates_slice, ssa_trend_f,
type="l", col = "magenta", lwd=2)
lines(dates_slice, cissa_trend,
type="l", col = "red", lwd=2)
# Легенда
legend("topleft", legend = c("Весь ряд", "CiSSA тренд", "SSA тренд (eossa)", "SSA тренд (fossa)"),
col = c("black", "red", "blue", "magenta"), lty = 1, lwd = 3)
plot(dates_slice, ssa_cycle,
main = "IP USA цикличность", xlab = "Время", ylab = "Значение",
type="l", col = "blue", ylim=c(-10, 10), lwd=2)
lines(dates_slice, cissa_cycle,
type="l", col = "red", lwd=2)
lines(dates_slice, ssa_cycle_f,
type="l", col = "magenta", lwd=2)
# Легенда
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"),
col = c("red", "blue", "magenta"), lty = 1, lwd = 3)
# Настройка графиков для отображения двух графиков один под другим с общей осью X
layout(matrix(c(1, 2), nrow = 2, byrow = TRUE), heights = c(1, 1.2))
# Построение первого графика
par(mar = c(2, 4, 2, 2)) # Уменьшение нижнего отступа
plot(dates_slice, ssa_sesonal, type = "l", col = "blue", lwd = 1,
main = "SSA (eossa) сезонность", xlab = "", ylab = "Значение")
# Добавление оси X внизу первого графика, но с пустыми метками
axis(1, labels = FALSE)
# Построение второго графика
par(mar = c(5, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, ssa_sesonal_f, type = "l", col = "magenta", lwd = 1,
main = "SSA (fossa) сезонность", xlab = "Время", ylab = "Значение")
par(mar = c(3, 4, 2, 2)) # Увеличение нижнего отступа
plot(dates_slice, cissa_sesonal, type = "l", col = "red", lwd = 1,
main = "CiSSA сезонность", xlab = "Время", ylab = "Значение")
# Восстановление макета по умолчанию
layout(1)
NA
NA
plot(dates_slice, ssa_residuals,
main = "IP USA остаток", xlab = "Время", ylab = "Значение",
type="l", col = "blue", ylim=c(-2, 2))
lines(dates_slice, cissa_residuals,
type="l", col = "red")
lines(dates_slice, ssa_residuals_f,
type="l", col = "magenta")
legend("topleft", legend = c("CiSSA", "SSA (eossa)", "SSA (fossa)"),
col = c("red", "blue", "magenta"), lty = 1, lwd = 3)
ssa_residuals |> density() |> plot()
cissa_residuals |> density() |> plot()
set.seed(100)
n_mse_tests <- function(n){
n <- 96*2-1
L <- 96
sigma <- 0.1
C <- 1
omega_cs <- 1/12
omega_sn <- 1/24
a <- 1/100
f_sum <- function(x){
f_const(x, C = C) +
f_cos(x, omega = omega_cs) +
f_exp(x, a = a) +
f_sin(x, omega = omega_sn)
}
f_C <- f_const |> generate_ts(n, C = C)
f_c <- f_cos |> generate_ts(n, omega = omega_cs)
f_s <- f_sin |> generate_ts(n, omega = omega_sn)
f_e <- f_exp |> generate_ts(n, a = a)
mse_lst <- list()
for (i in 1:n) {
f_noise <- rnorm(n, sd = sigma)
f_n <- f_sum(1:n) + f_noise
c <- circulant_SSA(f_n, L = L, extend_flag = TRUE)
# r <- c$t_series
r <- grouping_cissa(c, groups= list(trend = c(0, 1/1000),
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/10)
))
# mse_lst$cissa <- c(mse_lst$cissa, mse(f_sum(1:n), r[, 9] + r[, 5] + r[, 1]))
mse_lst$cissa <- c(mse_lst$cissa,
mse(f_sum(1:n),
r$trend + r$sesonal1 + r$sesonal2))
s <- ssa(f_n, L)
# e <- eossa(s, 1:10, k = 6)
e <- fossa(s)
g_sesonal <- grouping.auto(e, base = "eigen",
freq.bins = list(trend = 1/1000,
sesonal2 = c(1/25, 1/23),
sesonal1 = c(1/13, 1/10)
),
threshold = 0.5)
r <- reconstruct(e, groups=c(list(exp = 1, C = 2), g_sesonal))
mse_lst$ssa <-
c(mse_lst$ssa, mse(f_sum(1:n), r$trend + r$sesonal2 + r$sesonal1))
}
return(mse_lst)
}
res_mse_test <- n_mse_tests(10000)
# Оценка плотности
density_estimate_cissa <- density(res_mse_test$cissa)
# Построение графика плотности
plot(density_estimate_cissa, main = "Оценка плотности",
xlab = "Значение", ylab = "Плотность",
col = "blue", lwd = 2)
density_estimate_ssa <- density(res_mse_test$ssa)
# Построение графика плотности
plot(density_estimate_ssa, main = "Оценка плотности",
xlab = "Значение", ylab = "Плотность",
col = "blue", lwd = 2)
res_mse_test$cissa |> summary()
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.02299 0.03062 0.03345 0.03378 0.03575 0.04800
res_mse_test$cissa |> sd()
[1] 0.004333975
res_mse_test$ssa |> summary()
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000576 0.001710 0.002125 0.002228 0.002585 0.006311
res_mse_test$ssa |> sd()
[1] 0.0008283841
IP_values_slice |> extend(192) |> plot(type="l", lwd = 3)
c(rep(0, 192),IP_values_slice) |> lines(type="l", col="red")
n <- 96*2
L <- 96
x <- 0:(n-1)
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- y1 + y2
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
# y_main <- y
# X <- hankel(y)
# K <- dim(X)[2]
# res <- list()
# for (i in 1:K){
# y <- X[, i]
#
# # Выполняем быстрое преобразование Фурье
# fft_y <- fft(y)
#
# # Получаем амплитуды и фазы
# amplitudes <- Mod(fft_y)
# phases <- Arg(fft_y)
#
# res[[i]] <- reconstruct_fft(frequencies, amplitudes, phases)
# }
#
# nft <- res[[1]]
# print(nft |> length())
# res_full <- matrix(0, nrow = |> length(), )
#
# for (i in 1:K){
# res_full <-
# }
#
#
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
plot(x, Reduce("+", y_reconstructed), type = "l")
# lines(x, y, col = "red", type = "l", lty = 2)
x <- 1:100
y <- sin(2*pi*x)
dftmtx(10)[3, 2]
[1] 0.309017-0.9510565i
dftmtx(10)[2, 3]
[1] 0.309017-0.9510565i
(as.matrix(dftmtx(10)[3, ])) %*% t(as.matrix(Conj(dftmtx(10)[, 3])))
[,1] [,2] [,3] [,4] [,5]
[1,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[2,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[3,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[4,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000-0.0000000i 0.309017+0.9510565i
[5,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[6,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[7,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[8,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[9,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000-0.0000000i 0.309017+0.9510565i
[10,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[,6] [,7] [,8] [,9] [,10]
[1,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[2,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[3,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[4,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i
[5,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
[6,] 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i
[7,] 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i
[8,] -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i -0.809017+0.5877853i
[9,] -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i 0.309017+0.9510565i
[10,] 0.309017+0.9510565i -0.809017+0.5877853i -0.809017-0.5877853i 0.309017-0.9510565i 1.000000+0.0000000i
dim( t(as.matrix(Conj(dftmtx(10)[3, ]))))
[1] 1 10
dim(as.matrix(dftmtx(10)[3, ]))
[1] 10 1
X <- matrix(c(32, 21, 23,
521,631452, 25251,
1536, 75, 38), nrow= 3)
f_mat <- dftmtx(3) / sqrt(3)
f_mat_inv <- Conj(f_mat)
X
[,1] [,2] [,3]
[1,] 32 521 1536
[2,] 21 631452 75
[3,] 23 25251 38
f_mat %*% f_mat_inv %*% X
[,1] [,2] [,3]
[1,] 32+0i 521+0i 1536+0i
[2,] 21+0i 631452+0i 75+0i
[3,] 23+0i 25251+0i 38+0i
data_slice <- 1:538
n <- 96*2
L <- 96
x <- data_slice
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- IP_values[data_slice]
y_extended <- y |> extend(L)
x <- 1:length(y_extended)
y <- IP_values[data_slice]
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
data_slice <- 1:538
n <- 96*2
L <- 96
x <- data_slice
y1 <- cos(2 * pi / 12 * x) # Первая компонента
y2 <- sin(2 * pi / 48 * x) # Вторая компонента
# Создаем общий временной ряд
y <- IP_values[data_slice]
y_extended <- y |> extend(L)
x <- 1:length(y_extended)
y <- IP_values[data_slice]
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
# Индексы для частот
n <- length(y)
frequencies <- (0:(n-1)) / n
# Функция для восстановления компонент
reconstruct_fft <- function(frequencies, amplitudes, phases) {
reconstructed <- list()
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
reconstructed[[i]] <-
amplitudes[i] * cos(2 * pi * frequencies[i] * x + phases[i]) / n * 2
}
return(reconstructed)
}
y_reconstructed <- reconstruct_fft(frequencies, amplitudes, phases)
# Строим графики
for (i in 1:(n)){
plot(x, y_reconstructed[[i]], main = paste(frequencies[i]))
}
n <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]])
[,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
[2,] 2.515349e-17-3.469447e-18i 3.851860e-34+1.637040e-33i 1.734723e-18+6.505213e-18i -1.040834e-17-7.806256e-18i
[3,] -1.734723e-18+8.673617e-19i 1.213336e-32-9.629650e-35i -2.602085e-18+6.938894e-18i -1.040834e-17-2.645453e-17i
[4,] 1.387779e-17-6.722053e-18i 0.000000e+00-2.311116e-33i -6.765422e-17+1.734723e-18i 8.673617e-18+1.734723e-18i
[5,] -8.673617e-19+9.540979e-18i -3.851860e-34-4.188898e-33i 6.938894e-18+5.421011e-18i 0.000000e+00-7.372575e-18i
[6,] 5.000000e-01-0.000000e+00i -9.629650e-34-2.888895e-33i -8.673617e-19-8.023096e-18i 1.214306e-17-1.691355e-17i
[7,] -1.040834e-17-6.071532e-18i 1.224606e-16+0.000000e+00i 6.938894e-18+5.421011e-18i -1.040834e-17-8.239937e-18i
[8,] -8.673617e-19-2.406929e-17i -7.896313e-33+9.629650e-34i -5.000000e-01-0.000000e+00i -1.214306e-17+5.811324e-17i
[9,] -8.673617e-19+1.387779e-17i 9.629650e-34-5.488900e-33i -8.673617e-19+2.775558e-17i -8.660254e-01-0.000000e+00i
[10,] -8.673617e-19+2.385245e-18i -3.274081e-33-1.829633e-33i -2.255141e-17-4.987330e-18i -3.469447e-18+2.753874e-17i
[,10] [,11] [,12] [,13]
[1,] -8.673617e-18+1.821460e-17i -1.734723e-18-8.673617e-19i -8.673617e-19+1.734723e-18i 0.000000e+00-3.851860e-34i
[2,] 5.724587e-17+5.204170e-18i 7.806256e-18-1.040834e-17i 0.000000e+00+1.257675e-17i -3.851860e-34+2.311116e-33i
[3,] 1.734723e-18-6.071532e-18i 5.030698e-17-2.775558e-17i 1.734723e-18+4.336809e-18i -3.466674e-33-3.274081e-33i
[4,] -3.122502e-17+2.862294e-17i 6.938894e-18-6.071532e-18i 5.551115e-17+3.903128e-18i -7.703720e-34-4.237046e-33i
[5,] -2.255141e-17+2.255141e-17i 1.387779e-17-2.211772e-17i 8.673617e-19-3.469447e-18i 2.465190e-32+9.629650e-34i
[6,] -8.673617e-18+1.734723e-17i 2.255141e-17-3.035766e-18i 2.602085e-18+1.474515e-17i -1.540744e-33-1.155558e-33i
[7,] -6.938894e-18+3.035766e-18i -1.144917e-16+7.372575e-18i -2.602085e-18+2.168404e-18i -5.007418e-33+1.925930e-34i
[8,] -2.949030e-17-6.808790e-17i -8.673617e-18-2.558717e-17i -4.336809e-17+2.537033e-17i 3.466674e-33+1.540744e-33i
[9,] 1.734723e-18+7.719519e-17i 3.469447e-18-1.257675e-17i -2.602085e-18-2.081668e-17i 1.540744e-33+2.503709e-33i
[10,] -1.000000e+00-0.000000e+00i 2.081668e-17-9.887924e-17i 1.734723e-17-9.540979e-18i 5.007418e-33+3.851860e-33i
[,14] [,15] [,16] [,17]
[1,] 4.770490e-18-1.734723e-18i 6.938894e-18-1.734723e-18i 1.734723e-18-8.673617e-18i 1.214306e-17+3.469447e-18i
[2,] 1.647987e-17-1.604619e-17i 2.602085e-18+6.071532e-18i -1.734723e-18+3.469447e-18i 7.806256e-18-6.071532e-18i
[3,] 5.204170e-18+2.602085e-18i -1.561251e-17+2.428613e-17i 2.602085e-18-6.938894e-18i 0.000000e+00+9.540979e-18i
[4,] 0.000000e+00-4.770490e-18i -1.734723e-18-1.214306e-17i 8.673617e-19-2.602085e-17i 8.673617e-19+1.734723e-18i
[5,] 3.469447e-18-9.540979e-18i 1.734723e-18-1.734723e-18i 6.938894e-18+1.214306e-17i -4.423545e-17-3.469447e-18i
[6,] -8.239937e-17+0.000000e+00i 1.734723e-18-2.602085e-18i -1.734723e-18-2.602085e-18i 2.602085e-18+9.540979e-18i
[7,] -2.602085e-18-1.387779e-17i -1.422473e-16+9.540979e-18i 0.000000e+00+6.071532e-18i 1.561251e-17-1.040834e-17i
[8,] 1.734723e-18-1.387779e-17i 6.938894e-18-1.647987e-17i -1.994932e-16+1.734723e-18i 1.734723e-18+1.647987e-17i
[9,] -5.204170e-18-1.301043e-18i 3.469447e-18+2.732189e-17i -3.469447e-18+1.561251e-17i 5.204170e-17+0.000000e+00i
[10,] 2.688821e-17-2.818926e-18i 0.000000e+00+5.637851e-18i -2.602085e-17-7.979728e-17i 1.734723e-18-2.602085e-17i
[,18] [,19] [,20] [,21]
[1,] 1.301043e-18+3.469447e-18i 2.118523e-33+0.000000e+00i 1.734723e-18+4.336809e-18i 1.734723e-18+1.561251e-17i
[2,] 8.239937e-18-1.734723e-18i -5.777790e-34-1.925930e-33i 4.336809e-19+8.673617e-19i -4.336809e-18-3.469447e-18i
[3,] 0.000000e+00-8.673617e-19i 1.117039e-32+7.703720e-34i 2.168404e-18+8.673617e-19i -8.673617e-19+0.000000e+00i
[4,] -2.168404e-18+8.673617e-19i 1.925930e-33+0.000000e+00i -1.257675e-17-1.734723e-18i 5.204170e-18+1.040834e-17i
[5,] -1.301043e-18+0.000000e+00i 2.311116e-33+7.703720e-34i 4.336809e-18+1.734723e-18i -1.301043e-17-2.862294e-17i
[6,] -1.257675e-17-1.647987e-17i -3.851860e-34+4.622232e-33i 4.336809e-19+0.000000e+00i 1.734723e-18-2.602085e-18i
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[3,] 1.734723e-18-4.336809e-19i -1.387779e-17-2.775558e-17i -4.336809e-18+1.734723e-18i -7.806256e-18+8.673617e-19i
[4,] 0.000000e+00+4.336809e-19i -1.734723e-18+0.000000e+00i 2.602085e-18-6.938894e-18i 0.000000e+00+0.000000e+00i
[5,] -8.673617e-19+0.000000e+00i 8.673617e-19+0.000000e+00i 1.734723e-18+0.000000e+00i -1.734723e-18+6.938894e-18i
[6,] 2.081668e-17-1.040834e-17i 0.000000e+00+0.000000e+00i 0.000000e+00+8.673617e-19i -8.673617e-19+0.000000e+00i
[7,] 8.673617e-19+4.336809e-19i 1.214306e-17-2.081668e-17i 1.734723e-18-8.673617e-19i 7.806256e-18-8.673617e-19i
[8,] 0.000000e+00+0.000000e+00i -3.469447e-18-8.673617e-19i 1.561251e-17+6.938894e-18i -1.734723e-18+0.000000e+00i
[9,] 0.000000e+00-6.505213e-19i 0.000000e+00+4.336809e-19i 1.734723e-18-8.673617e-19i -1.734723e-18+6.071532e-18i
[10,] 6.938894e-18+6.938894e-18i 0.000000e+00-8.673617e-19i 1.734723e-18+0.000000e+00i 3.469447e-18+8.673617e-19i
[,66] [,67] [,68] [,69]
[1,] -4.336809e-19-8.673617e-19i 6.162976e-33+1.848893e-32i 6.505213e-19+0.000000e+00i 4.336809e-19-1.214306e-17i
[2,] 4.336809e-19-6.071532e-18i -9.244464e-33+1.232595e-32i 4.770490e-18-8.673617e-19i 8.673617e-19+0.000000e+00i
[3,] 1.301043e-18-1.734723e-18i -9.860761e-32+9.860761e-32i 1.301043e-18+0.000000e+00i -4.336809e-19-1.734723e-18i
[4,] -3.469447e-18+3.469447e-18i 1.232595e-32-3.081488e-32i -1.951564e-17+6.071532e-18i 3.469447e-18-3.469447e-18i
[5,] -1.734723e-18+0.000000e+00i 2.465190e-32-6.162976e-33i 3.903128e-18-2.602085e-18i 2.775558e-17-1.387779e-17i
[6,] -5.637851e-18+6.938894e-18i 6.162976e-33-1.232595e-32i 3.035766e-18+0.000000e+00i 0.000000e+00-8.673617e-19i
[7,] 1.734723e-18-4.336809e-19i -4.930381e-32+4.314083e-32i -4.336809e-19-8.673617e-19i 4.336809e-18+0.000000e+00i
[8,] -8.673617e-19+0.000000e+00i 0.000000e+00-1.232595e-32i 1.301043e-18+6.938894e-18i 0.000000e+00+8.673617e-19i
[9,] 0.000000e+00+0.000000e+00i 6.162976e-33-6.162976e-33i -8.673617e-19+0.000000e+00i 1.561251e-17+0.000000e+00i
[10,] 7.806256e-18+1.734723e-17i -1.232595e-32+0.000000e+00i 3.469447e-18-4.336809e-19i 1.734723e-18-8.673617e-19i
[,70] [,71] [,72] [,73]
[1,] 2.168404e-18+3.469447e-18i -6.938894e-18+1.734723e-18i 3.252607e-19+0.000000e+00i 0.000000e+00+0.000000e+00i
[2,] 8.673617e-19-2.775558e-17i -1.301043e-18+3.469447e-18i -2.168404e-19+0.000000e+00i -6.740755e-33+3.081488e-33i
[3,] 2.602085e-18+3.469447e-18i -1.214306e-17-6.938894e-18i -4.336809e-19-8.673617e-19i -3.851860e-34+3.081488e-33i
[4,] 1.734723e-18-5.204170e-18i -3.903128e-18+0.000000e+00i -5.637851e-18-6.938894e-18i 2.696302e-33+0.000000e+00i
[5,] -1.734723e-18-1.734723e-18i 6.071532e-18-1.734723e-18i -4.336809e-19+8.673617e-19i -2.157042e-32+0.000000e+00i
[6,] 1.474515e-17-2.775558e-17i 0.000000e+00+0.000000e+00i 4.336809e-19-8.673617e-19i -6.933348e-33+3.081488e-33i
[7,] 6.938894e-18-5.204170e-18i -4.163336e-17+1.387779e-17i -4.336809e-19-8.673617e-19i 8.474092e-33+0.000000e+00i
[8,] -1.734723e-18+0.000000e+00i 0.000000e+00-8.673617e-19i 1.387779e-17-1.301043e-17i 3.081488e-33+0.000000e+00i
[9,] 3.469447e-18-3.469447e-18i 0.000000e+00+0.000000e+00i -1.734723e-18+8.673617e-19i -2.465190e-32+1.232595e-32i
[10,] 0.000000e+00+1.040834e-17i -1.734723e-18+8.673617e-19i 0.000000e+00+0.000000e+00i 1.540744e-33+0.000000e+00i
[,74] [,75] [,76] [,77]
[1,] 1.084202e-18-8.673617e-19i -4.770490e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -1.344411e-17-2.775558e-17i
[2,] -6.830474e-18+0.000000e+00i -1.192622e-18+1.734723e-18i -1.734723e-18-6.938894e-18i -3.035766e-18+1.734723e-18i
[3,] -7.589415e-19-8.673617e-19i 4.141652e-17+1.387779e-17i 8.673617e-19-3.469447e-18i 7.372575e-18-1.734723e-18i
[4,] 2.168404e-19+3.469447e-18i 2.168404e-18-1.734723e-18i 2.862294e-17+1.734723e-18i -2.168404e-19+0.000000e+00i
[5,] 8.673617e-19-8.673617e-19i 4.770490e-18-1.734723e-18i -5.637851e-18+1.734723e-18i 4.293441e-17+1.734723e-18i
[6,] 1.973248e-17+6.071532e-18i 6.505213e-19+0.000000e+00i -6.505213e-18-1.734723e-18i -1.734723e-18+0.000000e+00i
[7,] 2.602085e-18-2.602085e-18i 1.301043e-18-1.734723e-18i -2.602085e-18+0.000000e+00i -2.168404e-18-6.938894e-18i
[8,] -8.673617e-19+0.000000e+00i 4.770490e-18-3.469447e-18i -1.431147e-17-1.734723e-18i -1.301043e-18+1.734723e-18i
[9,] -1.734723e-18+1.734723e-18i 4.336809e-18+0.000000e+00i 0.000000e+00+3.469447e-18i 1.387779e-17-1.387779e-17i
[10,] -6.505213e-18+8.673617e-19i -8.673617e-19-1.734723e-18i 8.673617e-19+1.734723e-18i 1.734723e-18-1.734723e-18i
[,78] [,79] [,80] [,81]
[1,] -1.517883e-18+8.673617e-19i 4.622232e-32+0.000000e+00i -2.602085e-18+1.734723e-18i 8.673617e-19+2.602085e-18i
[2,] 1.387779e-17-8.673617e-19i 5.238529e-32-4.930381e-32i 2.602085e-18+1.734723e-18i -2.602085e-18-3.469447e-18i
[3,] 4.336809e-19+2.602085e-18i 3.081488e-33+1.047706e-31i -8.673617e-19+3.469447e-18i -5.204170e-18-1.734723e-18i
[4,] 1.192622e-18+0.000000e+00i -3.389637e-32+2.465190e-32i -4.336809e-19+2.168404e-17i 6.071532e-18-3.469447e-18i
[5,] 4.336809e-19+0.000000e+00i -1.232595e-32+1.232595e-32i -2.168404e-19+3.469447e-18i -1.387779e-17+1.387779e-17i
[6,] -6.288373e-18+1.474515e-17i 1.232595e-32-2.465190e-32i -1.084202e-18+8.673617e-19i 3.903128e-18-3.469447e-18i
[7,] -2.602085e-18+1.734723e-18i 1.910523e-31-3.451266e-31i -2.818926e-18+1.734723e-18i 0.000000e+00+0.000000e+00i
[8,] 4.336809e-19+8.673617e-19i 1.540744e-32+0.000000e+00i -4.336809e-19+4.857226e-17i -1.734723e-18+1.734723e-18i
[9,] 1.951564e-18-1.734723e-18i -4.622232e-32+6.162976e-33i -8.673617e-19+8.673617e-19i 4.076600e-17+1.127570e-16i
[10,] 1.387779e-17+6.071532e-18i -3.081488e-33-1.232595e-32i -4.336809e-19+2.602085e-18i -8.673617e-19+0.000000e+00i
[,82] [,83] [,84] [,85]
[1,] 3.469447e-18+5.204170e-18i 8.673617e-19+8.673617e-19i -8.673617e-19+0.000000e+00i 1.540744e-33+0.000000e+00i
[2,] 1.908196e-17+2.255141e-17i -1.734723e-18+1.734723e-18i -2.168404e-18-8.673617e-19i 3.081488e-33+1.078521e-32i
[3,] -2.602085e-18+3.469447e-18i -1.734723e-18+2.255141e-17i -1.734723e-18+8.673617e-19i -3.081488e-33+5.238529e-32i
[4,] 1.734723e-18-3.469447e-18i 7.806256e-18+1.734723e-18i 1.734723e-18-1.127570e-17i 4.622232e-33+2.157042e-32i
[5,] 8.673617e-19-1.734723e-18i 5.204170e-18+0.000000e+00i 1.734723e-18+8.673617e-19i 1.032298e-31-6.162976e-33i
[6,] -1.301043e-17+2.775558e-17i -2.602085e-18-1.734723e-18i 0.000000e+00-6.938894e-18i 0.000000e+00-3.081488e-33i
[7,] -4.336809e-19+3.469447e-18i -1.387779e-17+1.734723e-18i 2.168404e-19-2.602085e-18i -9.244464e-33+0.000000e+00i
[8,] 5.637851e-18+0.000000e+00i -2.602085e-18+0.000000e+00i -7.155734e-18+6.938894e-18i -2.311116e-33-3.081488e-33i
[9,] 2.602085e-18-1.734723e-18i 0.000000e+00-1.734723e-18i 1.734723e-18+0.000000e+00i -3.851860e-33+0.000000e+00i
[10,] 2.949030e-17+6.765422e-17i 8.673617e-19-3.469447e-18i 4.336809e-19-8.673617e-19i 1.540744e-33-9.244464e-33i
[,86] [,87] [,88] [,89]
[1,] -1.734723e-18-2.602085e-18i 2.602085e-18+8.673617e-19i -1.734723e-18-1.561251e-17i 5.030698e-17+5.290907e-17i
[2,] 1.431147e-17+1.474515e-17i -8.673617e-19+5.204170e-18i 0.000000e+00+1.040834e-17i 4.336809e-18+8.673617e-19i
[3,] -8.673617e-19-1.734723e-18i -1.387779e-17-2.515349e-17i 1.734723e-18+3.469447e-18i 3.469447e-18-1.214306e-17i
[4,] -1.344411e-17-1.734723e-18i 5.204170e-18-6.071532e-18i 2.168404e-17+2.688821e-17i 2.602085e-18+8.673617e-18i
[5,] 3.035766e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -5.204170e-18-1.734723e-18i 5.464379e-17+2.775558e-17i
[6,] -2.818926e-17+2.602085e-17i 6.938894e-18-6.071532e-18i -8.673617e-19-1.040834e-17i -2.602085e-18-1.734723e-18i
[7,] -1.301043e-18-6.071532e-18i -5.377643e-17+2.862294e-17i -8.673617e-19-1.734723e-18i 8.673617e-19-1.127570e-17i
[8,] -2.602085e-18+2.602085e-18i 8.673617e-19-3.469447e-18i -7.112366e-17+5.724587e-17i 5.204170e-18+1.040834e-17i
[9,] 1.084202e-18-1.734723e-18i 8.673617e-19+0.000000e+00i -8.673617e-19+3.469447e-18i 1.474515e-17-2.602085e-17i
[10,] -2.168404e-19+6.071532e-18i -4.336809e-19-3.469447e-18i 2.602085e-18-3.469447e-18i 6.071532e-18-1.734723e-18i
[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
[1,] -1.040834e-17+2.168404e-18i 3.122502e-17+7.372575e-18i -1.561251e-17+5.009014e-17i
[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]
plot(1:L, res_comp_wise[[1]][, 2])
Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}
Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длины
n <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]])
[,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
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[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
[1,] -1.040834e-17+2.168404e-18i 3.122502e-17+7.372575e-18i -1.561251e-17+5.009014e-17i
[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]
plot(1:L, res_comp_wise[[1]][, 2])
Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}
Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длины
n <- 96*2-1
x <- 0:(n-1)
L <- 96
y <- sin(2*pi/12 * x)
X <- hankel(y, L)
Ft <- dftmtx(L) / sqrt(L)
Ft_inv <- t(Conj(Ft))
component_wise_mult <- function(index){
Ft %*% t(sweep(Ft_inv, 1, X[, index], '*'))
}
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, nrow = n, ncol = L)
for (i in 1:K){
res[i:(i+L-1), ] <- res[i:(i+L-1), ] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[i, ] <- res[i, ] / counters[i]
}
res
}
res_comp_wise <- lapply(1:L, component_wise_mult)
print(res_comp_wise[[1]])
[,1] [,2] [,3] [,4] [,5]
[1,] 0+0i 1.387779e-17-4.374756e-17i 2.255141e-17+1.778092e-17i -1.561251e-17+1.994932e-17i -5.377643e-17-6.505213e-18i
[2,] 0+0i 5.000000e-01+0.000000e+00i 6.938894e-18-6.776264e-17i 1.561251e-17-6.418477e-17i -6.938894e-18+1.170938e-17i
[3,] 0+0i 1.040834e-17-2.569559e-17i 8.660254e-01+0.000000e+00i -3.989864e-17-3.165870e-17i -5.898060e-17-3.361027e-17i
[4,] 0+0i -2.949030e-17+2.634611e-17i 6.938894e-17-2.667137e-17i 1.000000e+00-0.000000e+00i 2.949030e-17-1.994932e-17i
[5,] 0+0i 5.204170e-18-4.987330e-18i -1.734723e-17-2.602085e-18i 2.949030e-17+0.000000e+00i 8.660254e-01-0.000000e+00i
[6,] 0+0i 5.204170e-18+6.505213e-18i 0.000000e+00-3.187554e-17i -5.377643e-17-1.431147e-17i -3.469447e-18+1.144917e-16i
[7,] 0+0i 3.469447e-18-4.770490e-18i -2.775558e-17-4.336809e-19i -3.469447e-18-6.071532e-18i 2.255141e-17-2.168404e-18i
[8,] 0+0i -1.734723e-18+1.647987e-17i 0.000000e+00-8.673617e-18i -1.144917e-16+1.149254e-16i -6.938894e-18-1.214306e-17i
[9,] 0+0i 0.000000e+00+6.071532e-18i 1.734723e-18-5.637851e-18i 0.000000e+00+1.734723e-18i 5.204170e-17-1.301043e-17i
[10,] 0+0i -8.673617e-19-4.336809e-19i -5.204170e-18-5.204170e-18i 2.949030e-17+5.204170e-18i 1.040834e-17+3.469447e-18i
[,6] [,7] [,8] [,9]
[1,] 0.000000e+00+4.987330e-18i 5.777790e-34-3.274081e-33i -3.469447e-18+7.806256e-18i -2.602085e-18+0.000000e+00i
[2,] 2.515349e-17-3.469447e-18i 3.851860e-34+1.637040e-33i 1.734723e-18+6.505213e-18i -1.040834e-17-7.806256e-18i
[3,] -1.734723e-18+8.673617e-19i 1.213336e-32-9.629650e-35i -2.602085e-18+6.938894e-18i -1.040834e-17-2.645453e-17i
[4,] 1.387779e-17-6.722053e-18i 0.000000e+00-2.311116e-33i -6.765422e-17+1.734723e-18i 8.673617e-18+1.734723e-18i
[5,] -8.673617e-19+9.540979e-18i -3.851860e-34-4.188898e-33i 6.938894e-18+5.421011e-18i 0.000000e+00-7.372575e-18i
[6,] 5.000000e-01-0.000000e+00i -9.629650e-34-2.888895e-33i -8.673617e-19-8.023096e-18i 1.214306e-17-1.691355e-17i
[7,] -1.040834e-17-6.071532e-18i 1.224606e-16+0.000000e+00i 6.938894e-18+5.421011e-18i -1.040834e-17-8.239937e-18i
[8,] -8.673617e-19-2.406929e-17i -7.896313e-33+9.629650e-34i -5.000000e-01-0.000000e+00i -1.214306e-17+5.811324e-17i
[9,] -8.673617e-19+1.387779e-17i 9.629650e-34-5.488900e-33i -8.673617e-19+2.775558e-17i -8.660254e-01-0.000000e+00i
[10,] -8.673617e-19+2.385245e-18i -3.274081e-33-1.829633e-33i -2.255141e-17-4.987330e-18i -3.469447e-18+2.753874e-17i
[,10] [,11] [,12] [,13]
[1,] -8.673617e-18+1.821460e-17i -1.734723e-18-8.673617e-19i -8.673617e-19+1.734723e-18i 0.000000e+00-3.851860e-34i
[2,] 5.724587e-17+5.204170e-18i 7.806256e-18-1.040834e-17i 0.000000e+00+1.257675e-17i -3.851860e-34+2.311116e-33i
[3,] 1.734723e-18-6.071532e-18i 5.030698e-17-2.775558e-17i 1.734723e-18+4.336809e-18i -3.466674e-33-3.274081e-33i
[4,] -3.122502e-17+2.862294e-17i 6.938894e-18-6.071532e-18i 5.551115e-17+3.903128e-18i -7.703720e-34-4.237046e-33i
[5,] -2.255141e-17+2.255141e-17i 1.387779e-17-2.211772e-17i 8.673617e-19-3.469447e-18i 2.465190e-32+9.629650e-34i
[6,] -8.673617e-18+1.734723e-17i 2.255141e-17-3.035766e-18i 2.602085e-18+1.474515e-17i -1.540744e-33-1.155558e-33i
[7,] -6.938894e-18+3.035766e-18i -1.144917e-16+7.372575e-18i -2.602085e-18+2.168404e-18i -5.007418e-33+1.925930e-34i
[8,] -2.949030e-17-6.808790e-17i -8.673617e-18-2.558717e-17i -4.336809e-17+2.537033e-17i 3.466674e-33+1.540744e-33i
[9,] 1.734723e-18+7.719519e-17i 3.469447e-18-1.257675e-17i -2.602085e-18-2.081668e-17i 1.540744e-33+2.503709e-33i
[10,] -1.000000e+00-0.000000e+00i 2.081668e-17-9.887924e-17i 1.734723e-17-9.540979e-18i 5.007418e-33+3.851860e-33i
[,14] [,15] [,16] [,17]
[1,] 4.770490e-18-1.734723e-18i 6.938894e-18-1.734723e-18i 1.734723e-18-8.673617e-18i 1.214306e-17+3.469447e-18i
[2,] 1.647987e-17-1.604619e-17i 2.602085e-18+6.071532e-18i -1.734723e-18+3.469447e-18i 7.806256e-18-6.071532e-18i
[3,] 5.204170e-18+2.602085e-18i -1.561251e-17+2.428613e-17i 2.602085e-18-6.938894e-18i 0.000000e+00+9.540979e-18i
[4,] 0.000000e+00-4.770490e-18i -1.734723e-18-1.214306e-17i 8.673617e-19-2.602085e-17i 8.673617e-19+1.734723e-18i
[5,] 3.469447e-18-9.540979e-18i 1.734723e-18-1.734723e-18i 6.938894e-18+1.214306e-17i -4.423545e-17-3.469447e-18i
[6,] -8.239937e-17+0.000000e+00i 1.734723e-18-2.602085e-18i -1.734723e-18-2.602085e-18i 2.602085e-18+9.540979e-18i
[7,] -2.602085e-18-1.387779e-17i -1.422473e-16+9.540979e-18i 0.000000e+00+6.071532e-18i 1.561251e-17-1.040834e-17i
[8,] 1.734723e-18-1.387779e-17i 6.938894e-18-1.647987e-17i -1.994932e-16+1.734723e-18i 1.734723e-18+1.647987e-17i
[9,] -5.204170e-18-1.301043e-18i 3.469447e-18+2.732189e-17i -3.469447e-18+1.561251e-17i 5.204170e-17+0.000000e+00i
[10,] 2.688821e-17-2.818926e-18i 0.000000e+00+5.637851e-18i -2.602085e-17-7.979728e-17i 1.734723e-18-2.602085e-17i
[,18] [,19] [,20] [,21]
[1,] 1.301043e-18+3.469447e-18i 2.118523e-33+0.000000e+00i 1.734723e-18+4.336809e-18i 1.734723e-18+1.561251e-17i
[2,] 8.239937e-18-1.734723e-18i -5.777790e-34-1.925930e-33i 4.336809e-19+8.673617e-19i -4.336809e-18-3.469447e-18i
[3,] 0.000000e+00-8.673617e-19i 1.117039e-32+7.703720e-34i 2.168404e-18+8.673617e-19i -8.673617e-19+0.000000e+00i
[4,] -2.168404e-18+8.673617e-19i 1.925930e-33+0.000000e+00i -1.257675e-17-1.734723e-18i 5.204170e-18+1.040834e-17i
[5,] -1.301043e-18+0.000000e+00i 2.311116e-33+7.703720e-34i 4.336809e-18+1.734723e-18i -1.301043e-17-2.862294e-17i
[6,] -1.257675e-17-1.647987e-17i -3.851860e-34+4.622232e-33i 4.336809e-19+0.000000e+00i 1.734723e-18-2.602085e-18i
[7,] 0.000000e+00+1.734723e-18i -2.465190e-32-3.851860e-34i 4.336809e-19-8.673617e-19i 1.734723e-18-2.602085e-18i
[8,] 6.938894e-18+1.734723e-18i -1.540744e-33+3.851860e-34i -4.293441e-17+5.377643e-17i -8.673617e-19-6.071532e-18i
[9,] -8.673617e-19+3.469447e-18i 1.540744e-33-3.851860e-34i 2.602085e-18-3.035766e-18i -5.377643e-17+5.204170e-17i
[10,] -1.387779e-17+1.301043e-17i -7.703720e-34-6.933348e-33i 8.673617e-19+1.561251e-17i -2.602085e-18-5.204170e-18i
[,22] [,23] [,24] [,25]
[1,] 4.336809e-19+1.734723e-18i 6.071532e-18-5.204170e-18i -1.355253e-18-8.673617e-19i 0.000000e+00+0.000000e+00i
[2,] 1.214306e-17+1.387779e-17i -2.602085e-18+0.000000e+00i -2.602085e-18-8.673617e-19i -4.814825e-35+0.000000e+00i
[3,] 4.336809e-18-1.734723e-18i -4.163336e-17+0.000000e+00i 8.673617e-19-8.673617e-19i -3.274081e-33+0.000000e+00i
[4,] -1.734723e-18-1.387779e-17i 1.734723e-18-1.734723e-18i -1.994932e-17+0.000000e+00i 1.925930e-34+2.311116e-33i
[5,] 6.938894e-18+6.938894e-18i -4.336809e-19+6.938894e-18i 2.168404e-18+1.734723e-18i 0.000000e+00-2.311116e-33i
[6,] -5.464379e-17-5.204170e-17i 0.000000e+00+6.938894e-18i 2.602085e-18-2.602085e-18i -2.503709e-33+0.000000e+00i
[7,] 3.469447e-18-6.938894e-18i -4.336809e-17-5.724587e-17i 1.734723e-18-8.673617e-19i 3.851860e-34-2.311116e-33i
[8,] -1.734723e-18+2.255141e-17i -2.602085e-18-1.214306e-17i -4.119968e-17-1.127570e-17i -3.851860e-34-3.081488e-33i
[9,] -3.469447e-18+0.000000e+00i 1.734723e-18-8.673617e-19i 8.673617e-19-2.602085e-18i 0.000000e+00-7.703720e-34i
[10,] -8.847090e-17+5.464379e-17i -1.734723e-18-1.387779e-17i -4.336809e-19+1.734723e-18i -1.155558e-33+0.000000e+00i
[,26] [,27] [,28] [,29]
[1,] -2.710505e-19+0.000000e+00i 2.385245e-18+5.204170e-18i -1.734723e-18-3.469447e-18i 1.604619e-17+1.387779e-17i
[2,] 1.382358e-17-1.301043e-17i 6.071532e-18+6.938894e-18i 0.000000e+00-6.938894e-18i -4.336809e-19+1.734723e-18i
[3,] 5.421011e-20-8.673617e-19i 1.431147e-17+1.734723e-18i -8.673617e-19-3.469447e-18i -6.505213e-19+0.000000e+00i
[4,] 3.252607e-18-8.673617e-19i -1.517883e-18+0.000000e+00i -8.673617e-19+1.734723e-18i 8.673617e-19-1.734723e-18i
[5,] -8.673617e-19+2.602085e-18i 1.084202e-18+0.000000e+00i 2.168404e-18-1.734723e-18i -2.775558e-17-2.949030e-17i
[6,] 6.938894e-18+0.000000e+00i -4.336809e-19+1.734723e-18i -5.637851e-18+0.000000e+00i -1.301043e-18-1.734723e-18i
[7,] 4.553649e-18+3.469447e-18i 2.862294e-17-3.989864e-17i 2.602085e-18-1.734723e-18i 1.734723e-18+0.000000e+00i
[8,] 8.673617e-19+0.000000e+00i 2.602085e-18+1.734723e-18i 5.421011e-17+1.387779e-17i 3.469447e-18+3.469447e-18i
[9,] 4.336809e-19+1.734723e-18i -1.301043e-18+1.734723e-18i -3.469447e-18-1.734723e-18i 4.336809e-19+1.214306e-17i
[10,] 4.336809e-19-2.602085e-18i -1.734723e-18-3.469447e-18i 8.673617e-19+5.204170e-18i 6.505213e-18+5.204170e-18i
[,30] [,31] [,32] [,33]
[1,] 6.505213e-19+8.673617e-19i 0.000000e+00+0.000000e+00i 1.301043e-18-8.673617e-19i -2.688821e-17+0.000000e+00i
[2,] 7.155734e-18+8.673617e-19i 4.622232e-33-3.081488e-33i -4.336809e-19-8.673617e-19i -3.469447e-18+1.734723e-18i
[3,] 8.673617e-19+8.673617e-19i -2.619265e-32+0.000000e+00i 1.301043e-18+2.602085e-18i -6.938894e-18-1.734723e-18i
[4,] 1.084202e-18+0.000000e+00i 4.622232e-33+0.000000e+00i -6.505213e-19+7.806256e-18i 1.301043e-18+3.469447e-18i
[5,] -1.084202e-18+0.000000e+00i -2.696302e-32-1.540744e-32i 8.673617e-19+3.469447e-18i -1.474515e-17+0.000000e+00i
[6,] -5.854692e-18-2.168404e-17i -1.540744e-33+6.162976e-33i -2.168404e-19+0.000000e+00i -1.301043e-18+1.734723e-18i
[7,] -1.517883e-18-1.734723e-18i 2.187856e-31-4.930381e-32i -6.505213e-19-8.673617e-19i 5.637851e-18-1.734723e-18i
[8,] -3.035766e-18+3.469447e-18i -6.162976e-33+0.000000e+00i -6.505213e-18+2.081668e-17i -3.469447e-18-3.469447e-18i
[9,] 1.517883e-18+2.602085e-18i -2.465190e-32+3.081488e-33i 0.000000e+00+8.673617e-19i -6.722053e-17-2.775558e-17i
[10,] -6.505213e-19-6.071532e-18i -1.386670e-32-1.848893e-32i 2.168404e-19-3.469447e-18i -1.734723e-18-3.469447e-18i
[,34] [,35] [,36] [,37]
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[8,] -8.673617e-19+0.000000e+00i 4.770490e-18-3.469447e-18i -1.431147e-17-1.734723e-18i -1.301043e-18+1.734723e-18i
[9,] -1.734723e-18+1.734723e-18i 4.336809e-18+0.000000e+00i 0.000000e+00+3.469447e-18i 1.387779e-17-1.387779e-17i
[10,] -6.505213e-18+8.673617e-19i -8.673617e-19-1.734723e-18i 8.673617e-19+1.734723e-18i 1.734723e-18-1.734723e-18i
[,78] [,79] [,80] [,81]
[1,] -1.517883e-18+8.673617e-19i 4.622232e-32+0.000000e+00i -2.602085e-18+1.734723e-18i 8.673617e-19+2.602085e-18i
[2,] 1.387779e-17-8.673617e-19i 5.238529e-32-4.930381e-32i 2.602085e-18+1.734723e-18i -2.602085e-18-3.469447e-18i
[3,] 4.336809e-19+2.602085e-18i 3.081488e-33+1.047706e-31i -8.673617e-19+3.469447e-18i -5.204170e-18-1.734723e-18i
[4,] 1.192622e-18+0.000000e+00i -3.389637e-32+2.465190e-32i -4.336809e-19+2.168404e-17i 6.071532e-18-3.469447e-18i
[5,] 4.336809e-19+0.000000e+00i -1.232595e-32+1.232595e-32i -2.168404e-19+3.469447e-18i -1.387779e-17+1.387779e-17i
[6,] -6.288373e-18+1.474515e-17i 1.232595e-32-2.465190e-32i -1.084202e-18+8.673617e-19i 3.903128e-18-3.469447e-18i
[7,] -2.602085e-18+1.734723e-18i 1.910523e-31-3.451266e-31i -2.818926e-18+1.734723e-18i 0.000000e+00+0.000000e+00i
[8,] 4.336809e-19+8.673617e-19i 1.540744e-32+0.000000e+00i -4.336809e-19+4.857226e-17i -1.734723e-18+1.734723e-18i
[9,] 1.951564e-18-1.734723e-18i -4.622232e-32+6.162976e-33i -8.673617e-19+8.673617e-19i 4.076600e-17+1.127570e-16i
[10,] 1.387779e-17+6.071532e-18i -3.081488e-33-1.232595e-32i -4.336809e-19+2.602085e-18i -8.673617e-19+0.000000e+00i
[,82] [,83] [,84] [,85]
[1,] 3.469447e-18+5.204170e-18i 8.673617e-19+8.673617e-19i -8.673617e-19+0.000000e+00i 1.540744e-33+0.000000e+00i
[2,] 1.908196e-17+2.255141e-17i -1.734723e-18+1.734723e-18i -2.168404e-18-8.673617e-19i 3.081488e-33+1.078521e-32i
[3,] -2.602085e-18+3.469447e-18i -1.734723e-18+2.255141e-17i -1.734723e-18+8.673617e-19i -3.081488e-33+5.238529e-32i
[4,] 1.734723e-18-3.469447e-18i 7.806256e-18+1.734723e-18i 1.734723e-18-1.127570e-17i 4.622232e-33+2.157042e-32i
[5,] 8.673617e-19-1.734723e-18i 5.204170e-18+0.000000e+00i 1.734723e-18+8.673617e-19i 1.032298e-31-6.162976e-33i
[6,] -1.301043e-17+2.775558e-17i -2.602085e-18-1.734723e-18i 0.000000e+00-6.938894e-18i 0.000000e+00-3.081488e-33i
[7,] -4.336809e-19+3.469447e-18i -1.387779e-17+1.734723e-18i 2.168404e-19-2.602085e-18i -9.244464e-33+0.000000e+00i
[8,] 5.637851e-18+0.000000e+00i -2.602085e-18+0.000000e+00i -7.155734e-18+6.938894e-18i -2.311116e-33-3.081488e-33i
[9,] 2.602085e-18-1.734723e-18i 0.000000e+00-1.734723e-18i 1.734723e-18+0.000000e+00i -3.851860e-33+0.000000e+00i
[10,] 2.949030e-17+6.765422e-17i 8.673617e-19-3.469447e-18i 4.336809e-19-8.673617e-19i 1.540744e-33-9.244464e-33i
[,86] [,87] [,88] [,89]
[1,] -1.734723e-18-2.602085e-18i 2.602085e-18+8.673617e-19i -1.734723e-18-1.561251e-17i 5.030698e-17+5.290907e-17i
[2,] 1.431147e-17+1.474515e-17i -8.673617e-19+5.204170e-18i 0.000000e+00+1.040834e-17i 4.336809e-18+8.673617e-19i
[3,] -8.673617e-19-1.734723e-18i -1.387779e-17-2.515349e-17i 1.734723e-18+3.469447e-18i 3.469447e-18-1.214306e-17i
[4,] -1.344411e-17-1.734723e-18i 5.204170e-18-6.071532e-18i 2.168404e-17+2.688821e-17i 2.602085e-18+8.673617e-18i
[5,] 3.035766e-18+0.000000e+00i -1.734723e-18-1.734723e-18i -5.204170e-18-1.734723e-18i 5.464379e-17+2.775558e-17i
[6,] -2.818926e-17+2.602085e-17i 6.938894e-18-6.071532e-18i -8.673617e-19-1.040834e-17i -2.602085e-18-1.734723e-18i
[7,] -1.301043e-18-6.071532e-18i -5.377643e-17+2.862294e-17i -8.673617e-19-1.734723e-18i 8.673617e-19-1.127570e-17i
[8,] -2.602085e-18+2.602085e-18i 8.673617e-19-3.469447e-18i -7.112366e-17+5.724587e-17i 5.204170e-18+1.040834e-17i
[9,] 1.084202e-18-1.734723e-18i 8.673617e-19+0.000000e+00i -8.673617e-19+3.469447e-18i 1.474515e-17-2.602085e-17i
[10,] -2.168404e-19+6.071532e-18i -4.336809e-19-3.469447e-18i 2.602085e-18-3.469447e-18i 6.071532e-18-1.734723e-18i
[,90] [,91] [,92] [,93]
[1,] -6.071532e-18+5.204170e-18i -4.314083e-32-3.081488e-32i 8.673617e-18-2.385245e-18i -1.214306e-17+3.035766e-18i
[2,] -1.214306e-17+1.301043e-18i -8.628166e-32-3.081488e-32i 1.734723e-18-2.168404e-18i 2.081668e-17+1.734723e-18i
[3,] 1.734723e-18-7.806256e-18i -2.095412e-31+1.848893e-32i 0.000000e+00+8.673617e-19i 1.040834e-17-3.079134e-17i
[4,] -6.071532e-18-6.938894e-18i 1.232595e-32-1.848893e-32i 0.000000e+00-8.673617e-19i 1.734723e-18-8.673617e-19i
[5,] 4.336809e-18-4.336809e-19i -4.930381e-32+1.047706e-31i -1.734723e-18-4.336809e-18i -5.637851e-17+2.775558e-17i
[6,] 4.119968e-17+2.775558e-17i 1.232595e-32+1.232595e-32i 6.938894e-18-9.107298e-18i -1.734723e-18+3.469447e-18i
[7,] 2.602085e-18-2.602085e-18i 5.916457e-31+1.232595e-32i -8.673617e-19-1.734723e-18i 6.938894e-18+0.000000e+00i
[8,] -2.602085e-18-6.938894e-18i 1.848893e-32-6.779273e-32i 3.989864e-17+2.515349e-17i -1.734723e-18-8.673617e-19i
[9,] 3.035766e-18-8.673617e-19i -5.546678e-32+9.860761e-32i 4.336809e-18+0.000000e+00i 6.852158e-17+1.734723e-18i
[10,] 4.336809e-19-8.673617e-19i 0.000000e+00+6.162976e-33i 2.602085e-18+5.204170e-18i 1.734723e-18+7.806256e-18i
[,94] [,95] [,96]
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[2,] -5.724587e-17-1.205633e-16i 8.673617e-18+4.163336e-17i -1.734723e-18-2.688821e-17i
[3,] -2.081668e-17+2.602085e-18i 5.551115e-17-5.637851e-17i -1.734723e-18+1.214306e-17i
[4,] -6.938894e-18+5.030698e-17i 0.000000e+00+1.040834e-17i 2.862294e-17-2.797242e-17i
[5,] -6.938894e-18+3.469447e-18i 1.734723e-17+2.341877e-17i 8.673617e-19+5.637851e-18i
[6,] -1.092876e-16+4.336809e-18i -1.734723e-18-1.040834e-17i 8.673617e-19-1.734723e-18i
[7,] 3.469447e-18-1.561251e-17i -2.428613e-17+5.030698e-17i 3.469447e-18-3.903128e-18i
[8,] -3.469447e-18+2.775558e-17i 1.127570e-17+8.673617e-18i -2.949030e-17+2.255141e-17i
[9,] 0.000000e+00-1.734723e-18i -1.387779e-17-8.673617e-19i 2.602085e-18+4.770490e-18i
[10,] 2.775558e-17-3.209238e-17i -8.673617e-19-1.040834e-17i -8.673617e-19-1.301043e-17i
[ достигнута getOption("max.print") -- пропущено 86 строк ]
plot(1:L, res_comp_wise[[1]][, 2])
Предупреждение в xy.coords(x, y, xlabel, ylabel, log) :
мнимые части убраны при преобразовании
avr <- averaging(res_comp_wise)
for (i in 1:dim(res$t_series)[2]){
plot(x, avr[i, ])
}
Ошибка в 1:dim(res$t_series)[2] :аргумент нулевой длины
# Ft %*% sweep(Ft_inv, 1, X[, 1], '*')[2, ]
reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- 96*2-1
x <- 0:(n-1)
L <- 48
frequencies <- (0:(L-1)) / L
y <- sin(2*pi/12 * x)
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
plot(x_main, rs$t_series[, 5])
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series
reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- 537
x <- 0:(n-1)
L <- 192
frequencies <- (0:(L-1)) / L
y <- IP_values_slice
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
# plot(x_main, rs$t_series[, 5])
for (i in 1:dim(r)[2]){
plot(1:n, rs$t_series[, i], col= "red", type = "l")
lines(1:n, r[, i])
}
cissa_like_fourier_transform <- function(ts, L){
reconstruct_fft <- function(x, y, frequencies) {
# Выполняем быстрое преобразование Фурье
fft_y <- fft(y)
# Получаем амплитуды и фазы
amplitudes <- Mod(fft_y)
phases <- Arg(fft_y)
reconstructed <- matrix(0, length(amplitudes), length(x))
n <- length(amplitudes)
for (i in 1:(length(amplitudes))) {
# print(i)
reconstructed[i, ] <-
amplitudes[i] *
cos(2 * pi * frequencies[i] * (x) + phases[i]) /
n
}
# plot(x, reconstructed[9, ], main = paste(x[1]), type = "l", col = "red")
# lines(x, y/2)
# plot(x, reconstructed[L+2-9, ], main = paste(x[1]))
return(reconstructed)
}
n <- length(ts)
x <- 0:(n-1)
L <- L
frequencies <- (0:(L-1)) / L
y <- ts
y_main <- y
x_main <- x
X <- hankel(y, L)
K <- dim(X)[2]
res <- list()
for (i in 1:K){
y <- X[, i]
x <- x_main[1:(1 + L - 1)]
res[[i]] <- reconstruct_fft(x, y, frequencies)
}
# for (i in 1:L){
# plot(x, res[[i]][9, ])
# }
res_mult <- res
# res
averaging <- function(res_comp_wise_mult){
K <- dim(X)[2]
counters <- rep(0, n)
res <- matrix(0, ncol = n, nrow = L)
for (i in 1:length(res_comp_wise_mult)){
res[, i:(i+L-1)] <- res[, i:(i+L-1)] + res_comp_wise_mult[[i]]
counters[i:(i+L-1)] <- counters[i:(i+L-1)] + 1
}
for (i in 1:n){
res[, i] <- res[, i] / counters[i]
}
res
}
avr <- averaging(res_mult)
group_by_elementary_freq_foureir <- function(res_averaged){
nf2 <- 0
if (L %% 2) {
nf2 <- (L + 1) / 2 - 1
} else {
nf2 <- L / 2 - 1
}
nft <- nf2 + abs((L %% 2) - 2)
Z <- matrix(0, ncol = nft, nrow = n)
# print(Z |> dim())
# print(res_averaged |> dim())
Z[, 1] <- res_averaged[1, ]
for (k in 1:nf2) {
Z[, k + 1] <- res_averaged[k + 1, ] + res_averaged[L + 2 - (k + 1), ]
}
if (L %% 2 != 0) {
Z[, nft] <- res_averaged[nft, ]
}
return(list(
t_series = Z,
freq = (0:dim(Z)[2])/L
))
}
rs <- group_by_elementary_freq_foureir(avr)
return(rs)
}
data_slice <- 1:537
dates_slice <- dates[data_slice]
IP_values_slice <- IP_values[data_slice]
eps <- 1/193
c <- circulant_SSA(IP_values_slice, L = 192, extend_flag = FALSE)
r <- c$t_series
c_ft <- cissa_like_fourier_transform(IP_values_slice, L = 192)
r_ft <- c_ft$t_series
for (i in 1:dim(r)[2]){
plot(1:n, r_ft[, i], col= "red", type = "l", lwd = 2)
lines(1:n, r[, i])
}